# Work on Moduli and Geometric Invariant Theory (except Abelian Varieties)

Moduli spaces are essentially maps. In an ordinary map, a point on a piece of paper corresponds to a location on the earth. Similarly, a point in a moduli space corresponds to an object of some kind, a variety or bundle or something more elaborate. The set of all these objects is thus put together in this fine but rather intangible 'map' known as a moduli space. That's why I have put a map of part of Maine in the background.

- An Elementary theorem in Geometric Invariant Theory,
*Bull. Amer. Math. Soc.*, 1961, pp. 483-487. Scanned reprint and DASH reprint - Topics in the Theory of Moduli, (published in Japanese),
*Sugaku*, 1963. Scanned English manuscript - Projective Invariants of Projective Structures,
*International Congress of Mathematicians, Stockholm 1962*, 1963, pp. 526-530. Scanned reprint - The Boundary of Moduli Schemes, mimeographed notes from the 1964 Woods Hole Symposium on Algebraic Geometry. Scanned manuscript
- Picard Groups of Moduli Problems, in
*Arithmetic Algebraic Geometry*, (Proceedings of a Conference in Purdue, 1963), Harper and Row, 1965. Scanned reprint - Two Fundamental Theorem on Deformations of Polarized Varieties (with T. Matsusaka),
*Amer. J. of Math.*, 1964, pp. 668-684. Scanned reprint and DASH reprint -
*Geometric Invariant Theory*, Springer-Verlag, 1965; 2nd enlarged edition, (with John Fogarty), 1982; 3rd enlarged edition, (with Frances Kirwan and John Fogarty), 1994, DejaVu - Abelian Quotients of the Teichmuller Modular Group,
*Journal d'Analyse*, 1967,**28**, pp. 227-244. Scanned reprint - Periods of Moduli Spaces of Bundles on Curves (with P. Newstead),
*Amer. J. of Math.*, 1968,**90**, pp. 1200-1208. Scanned reprint and DASH reprint - The Irreducibility of the Space of Curves of Given Genus (with P. Deligne),
*Publ. Math. de l'I.H.E.S.*, 1969,**36**, pp. 75-109. Scanned reprint and DASH reprint - A Remark on Mahler's Compactness Theorem,
*Proc. Amer. Math. Soc.*, 1971,**28**, pp. 289-194. Scanned reprint and DASH reprint - The Structure of the Moduli Spaces of Curves and Abelian Varieties,
*Actes du Congress Int. du Math.*, Nice, 1970; Gauthier-Villars, 1971. Scanned reprint - Introduction to the Theory of Moduli (with K. Suominen), in
*Algebraic Geometry, Oslo 1970*F. Oort editor, Wolters-Noordhoff, 1972, pp. 171-222.Scanned reprint - Matsusaka's Big Theorem (with D. Lieberman), in
*Algebraic Geometry, Arcata 1974*, AMS Proc. of Symposia in Pure Math.,**29**, 1975, pp. 513-530. Scanned reprint - The projectivity of the moduli space of stable curves, I: Preliminaries on "det" and "Div" (with F. Knudsen),
*Math. Scand.*,**39**, 1976, pp.19-55.

The projectivity of the moduli space of stable curves, II: the stacks*M*(sequel by F. Knudsen),_{g,n}*Math. Scand.*,**52**, 1983, pp.161-199.

The projectivity of the moduli space of stable curves III: the line bundles on*M*and a proof of trhe projectivity of the completion of_{g,n}*M*in characteristic 0 (sequel by F. Knudsen),_{g,n}*Math. Scand.*,**52**, 1983, pp.200-212. Scanned reprint - Stability of Projective Varieties, Monographie No. 24 de
*L'Enseignement Math.*,**23**, 1977, pp. 39-110. Scanned reprint - On the Kodaira Dimension of the Moduli Space of Curves (with Joe Harris and an appendix by William Fulton),
*Inv. Math.*, 1982, pp.23-88. Scanned reprint and DASH reprint - Towards an Enumerative Geometry of Moduli Space of Curves, in
*Arithmetic and Geometry*, edited by M. Artin, J. Tate, Birkhauser-Boston, 1983, pp.271-326. Scanned reprint - A Stratification of the Null Cone via the Moment Map (with Linda Ness),
*Amer. J. of Math.*,**106**, 1984, pp.1281-1329. Scanned reprint and DASH reprint